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Count trailing zeros in factorial of a number in C++

Given an integer number as input. The goal is to find the number of trailing zeroes in the factorial calculated for that number. A factorial of a number N is a product of all numbers in the range [1, N].

We know that we get a trailing zero only if the number is multiple of 10 or has a factor pair (2,5). In all factorials of any number greater than 5, we have a number of 2s more than 5s in prime factorization of that number. Dividing a number by powers of 5 will give us the count of 5s in its factors. So, the number of 5s will tell us the number of trailing zeroes.

For Example

number=6

Count of trailing zeros in factorial of a number are: 1

The factorial is 30.
Prime factors of 30 : 2 * 3 * 5
So only one pair of (2,5) exists so trailing zeros is 1.

number=12

Count of trailing zeros in factorial of a number are: 2

The factorial is 479001600.
Prime factors of 479001600 : 210 x 35 x 52 x 71 x 111
So we can get 2 pairs of (2,5) so trailing zeros are 2

Approach used in the below program is as follows −

In this approach we will divide the number by powers of 5. If it results in more than 1 then the number of trailing zeros will be the number of 5s. Add this to count.

• Take an integer number as input.

• Function trailing_zeros(int number) takes number and returns the count of trailing zeroes in factorial of number.

• Take the initial count as 0.

• Using a for loop, divide the number by powers of 5.

• If number/i is greater than 1, add this value to count.

• Return count as result at the end of loop.

 Live Demo

#include <iostream>
using namespace std;
int trailing_zeros(int number){
   int count = 0;
   for (int i = 5; number / i >= 1; i *= 5){
      int temp = number / i;
      count = count + temp;
   }
   return count;
}
int main(){
   int number = 50;
   cout<<"Count of trailing zeros in factorial of a number are: "<<trailing_zeros(number);
   return 0;
}

If we run the above code it will generate the following output −

Count of trailing zeros in factorial of a number are: 12

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